Self-organizing maps (SOMs) [1]}, [2]}
are widely used for unsupervised classification.
They map points in the input N-dimensional data space
\({\cal R}^{N}\)  into an array of cells or principal elements (PEs) in a
classification space \(\cal {A}\)  of reduced dimensionality (usually one or
two dimensions). The algorithm is designed to make
the output of the SOM reproduce, as much as possible, the topological
structure of the input distribution. In particular it attempts to map
adjacent clusters in the input space into adjacent PEs
(or more commonly, adjacent blocks of contiguous PEs) in the output space.
A variety of measures have been
proposed to evaluate the degree to which topology is preserved by a
particular mapping [3]}, [4]}, [5]}.
